Question

Consider the ray diagram for the refraction given below. The maximum value of angle $\theta$ for which the light suffers total internal reflection at the vertical surface, is

• A. ${\cos }^{-1}\left(\frac{3}{4}\right)$
• B. ${\sin }^{-1}\left(\frac{3}{4}\right)$
• C. ${\tan }^{-1}\left(\frac{4}{3}\right)$
• D. ${\cos }^{-1}\left(\frac{4}{3}\right)$

Answer 1

Answer: (B)

The critical angle for this case is
${\theta }^{\prime \prime }={\sin }^{-1}\frac{1}{1\cdot 25}={\sin }^{-1}\frac{4}{5}$
or $\sin {\theta }^{\prime \prime }=\frac{4}{5}$
Since, ${\theta }^{\prime \prime }=\frac{\pi }{2}-{\theta }^{\prime }$,
we have $\sin {\theta }^{\prime }=\cos {\theta }^{\prime \prime }=3/5$.
From Snell's law,
$\frac{\sin \theta }{\sin {\theta }^{\prime }}=1.25$
or $\sin \theta =1.25\times \sin {\theta }^{\prime }$
$=1.25\times \frac{3}{5}=\frac{3}{4}$
$\Rightarrow \theta ={\sin }^{-1}(3/4)$